By comparison with existing mean-field limit results, Theorem REF  gives rigorous justifications for both \(L\rightarrow \infty \)  and \(M\rightarrow \infty \) . By contrast, [1]}, [2]}, [3]} consider \(M\rightarrow \infty \)  with \(L\)  fixed.
In most results for NTK [4]}, [5]}, [6]}, [7]}, the size of \(M\)  grows as \(L\)  increases, while our results have these two parameters independent of each other. Furthermore, we have no requirement on the number of training samples.
